Measurements of Zγ* production are presented using data collected by the DELPHI detector at centre-of-mass energies ranging from 183 to 209 GeV, corresponding to an integrated luminosity of about 667 pb-1. The measurements cover a wide range of the possible final state four-fermion configurations: hadronic and leptonic (e+e-qq&#772;, μ+μ-qq&#772;, qq&#772;νν&#772;), fully leptonic (l+l-l+l-) and fully hadronic final states (qq&#772;qq&#772;, with a low mass qq&#772; pair). Measurements of the Zγ* cross-section for the various final states have been compared with the Standard Model expectations and found to be consistent within the errors. In addition, a total cross-section measurement of the l+l-l+l- cross-section is reported, and found to be in agreement with the prediction of the Standard Model.